0.94/1.15 YES 0.94/1.15 0.94/1.15 Problem 1: 0.94/1.15 0.94/1.15 (VAR x x0 y z) 0.94/1.15 (STRATEGY CONTEXTSENSITIVE 0.94/1.15 (*top*_0 1) 0.94/1.15 (cons_0 1 2) 0.94/1.15 (cons_1) 0.94/1.15 (s_0 1) 0.94/1.15 (big_0) 0.94/1.15 (inf_1) 0.94/1.15 ) 0.94/1.15 (RULES 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 ) 0.94/1.15 0.94/1.15 Problem 1: 0.94/1.15 0.94/1.15 Dependency Pairs Processor: 0.94/1.15 -> Pairs: 0.94/1.15 *TOP*_0(inf_1(x)) -> *TOP*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 *TOP*_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 *TOP*_0(inf_1(x)) -> x 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 CONS_0(inf_1(x),x0) -> x 0.94/1.15 CONS_0(x0,inf_1(x)) -> CONS_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> x 0.94/1.15 -> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 -> Unhiding Rules: 0.94/1.15 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.15 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.15 s_0(x) -> S_0(x) 0.94/1.15 0.94/1.15 Problem 1: 0.94/1.15 0.94/1.15 SCC Processor: 0.94/1.15 -> Pairs: 0.94/1.15 *TOP*_0(inf_1(x)) -> *TOP*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 *TOP*_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 *TOP*_0(inf_1(x)) -> x 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 CONS_0(inf_1(x),x0) -> x 0.94/1.15 CONS_0(x0,inf_1(x)) -> CONS_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> x 0.94/1.15 -> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 -> Unhiding rules: 0.94/1.15 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.15 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.15 s_0(x) -> S_0(x) 0.94/1.15 ->Strongly Connected Components: 0.94/1.15 ->->Cycle: 0.94/1.15 ->->-> Pairs: 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 CONS_0(inf_1(x),x0) -> x 0.94/1.15 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> x 0.94/1.15 ->->-> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 ->->-> Unhiding rules: 0.94/1.15 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.15 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.15 s_0(x) -> S_0(x) 0.94/1.15 ->->Cycle: 0.94/1.15 ->->-> Pairs: 0.94/1.15 *TOP*_0(inf_1(x)) -> *TOP*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 ->->-> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 ->->-> Unhiding rules: 0.94/1.15 Empty 0.94/1.15 0.94/1.15 0.94/1.15 The problem is decomposed in 2 subproblems. 0.94/1.15 0.94/1.15 Problem 1.1: 0.94/1.15 0.94/1.15 Reduction Pairs Processor: 0.94/1.15 -> Pairs: 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 CONS_0(inf_1(x),x0) -> x 0.94/1.15 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> x 0.94/1.15 -> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 -> Unhiding rules: 0.94/1.15 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.15 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.15 s_0(x) -> S_0(x) 0.94/1.15 -> Usable rules: 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 ->Interpretation type: 0.94/1.15 Linear 0.94/1.15 ->Coefficients: 0.94/1.15 All rationals 0.94/1.15 ->Dimension: 0.94/1.15 1 0.94/1.15 ->Bound: 0.94/1.15 2 0.94/1.15 ->Interpretation: 0.94/1.15 0.94/1.15 [cons_0](X1,X2) = X1 + 1/2.X2 0.94/1.15 [cons_1](X1,X2) = 1/2.X2 0.94/1.15 [s_0](X) = X + 1/2 0.94/1.15 [big_0] = 0 0.94/1.15 [inf_1](X) = 2.X + 2 0.94/1.15 [CONS_0](X1,X2) = X1 + 1/2.X2 0.94/1.15 [S_0](X) = X + 1/2 0.94/1.15 0.94/1.15 Problem 1.1: 0.94/1.15 0.94/1.15 SCC Processor: 0.94/1.15 -> Pairs: 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 CONS_0(inf_1(x),x0) -> x 0.94/1.15 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> x 0.94/1.15 -> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 -> Unhiding rules: 0.94/1.15 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.15 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.15 s_0(x) -> S_0(x) 0.94/1.15 ->Strongly Connected Components: 0.94/1.15 ->->Cycle: 0.94/1.15 ->->-> Pairs: 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 CONS_0(inf_1(x),x0) -> x 0.94/1.15 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> x 0.94/1.15 ->->-> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 ->->-> Unhiding rules: 0.94/1.15 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.15 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.15 s_0(x) -> S_0(x) 0.94/1.15 0.94/1.15 Problem 1.1: 0.94/1.15 0.94/1.15 Reduction Pairs Processor: 0.94/1.15 -> Pairs: 0.94/1.15 CONS_0(inf_1(x),x0) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 CONS_0(inf_1(x),x0) -> x 0.94/1.15 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 S_0(inf_1(x)) -> x 0.94/1.15 -> Rules: 0.94/1.15 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 -> Unhiding rules: 0.94/1.15 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.15 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.15 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.15 s_0(x) -> S_0(x) 0.94/1.15 -> Usable rules: 0.94/1.15 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.15 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.15 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.15 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.15 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.15 ->Interpretation type: 0.94/1.15 Linear 0.94/1.15 ->Coefficients: 0.94/1.15 All rationals 0.94/1.15 ->Dimension: 0.94/1.15 1 0.94/1.15 ->Bound: 0.94/1.15 2 0.94/1.15 ->Interpretation: 0.94/1.15 0.94/1.15 [cons_0](X1,X2) = X1 + X2 0.94/1.15 [cons_1](X1,X2) = X1 + 1/2.X2 0.94/1.16 [s_0](X) = 1/2.X 0.94/1.16 [big_0] = 0 0.94/1.16 [inf_1](X) = 2.X + 2 0.94/1.16 [CONS_0](X1,X2) = X1 0.94/1.16 [S_0](X) = 1/2.X 0.94/1.16 0.94/1.16 Problem 1.1: 0.94/1.16 0.94/1.16 SCC Processor: 0.94/1.16 -> Pairs: 0.94/1.16 CONS_0(inf_1(x),x0) -> x 0.94/1.16 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 ->Strongly Connected Components: 0.94/1.16 ->->Cycle: 0.94/1.16 ->->-> Pairs: 0.94/1.16 CONS_0(inf_1(x),x0) -> x 0.94/1.16 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 ->->-> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 ->->-> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 0.94/1.16 Problem 1.1: 0.94/1.16 0.94/1.16 Reduction Pairs Processor: 0.94/1.16 -> Pairs: 0.94/1.16 CONS_0(inf_1(x),x0) -> x 0.94/1.16 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 -> Usable rules: 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 ->Interpretation type: 0.94/1.16 Linear 0.94/1.16 ->Coefficients: 0.94/1.16 All rationals 0.94/1.16 ->Dimension: 0.94/1.16 1 0.94/1.16 ->Bound: 0.94/1.16 2 0.94/1.16 ->Interpretation: 0.94/1.16 0.94/1.16 [cons_0](X1,X2) = X1 + 1/2.X2 0.94/1.16 [cons_1](X1,X2) = X1 + 1/2.X2 0.94/1.16 [s_0](X) = X + 1 0.94/1.16 [big_0] = 0 0.94/1.16 [inf_1](X) = 2.X + 2 0.94/1.16 [CONS_0](X1,X2) = X1 0.94/1.16 [S_0](X) = 1/2.X + 1 0.94/1.16 0.94/1.16 Problem 1.1: 0.94/1.16 0.94/1.16 SCC Processor: 0.94/1.16 -> Pairs: 0.94/1.16 S_0(inf_1(x)) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x))) -> CONS_0(x,inf_1(s_0(x))) 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 ->Strongly Connected Components: 0.94/1.16 ->->Cycle: 0.94/1.16 ->->-> Pairs: 0.94/1.16 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 ->->-> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 ->->-> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 0.94/1.16 Problem 1.1: 0.94/1.16 0.94/1.16 Reduction Pairs Processor: 0.94/1.16 -> Pairs: 0.94/1.16 S_0(inf_1(x)) -> S_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 -> Usable rules: 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 ->Interpretation type: 0.94/1.16 Linear 0.94/1.16 ->Coefficients: 0.94/1.16 All rationals 0.94/1.16 ->Dimension: 0.94/1.16 1 0.94/1.16 ->Bound: 0.94/1.16 2 0.94/1.16 ->Interpretation: 0.94/1.16 0.94/1.16 [cons_0](X1,X2) = X1 + 1/2.X2 0.94/1.16 [cons_1](X1,X2) = 1/2.X1 + 1/2 0.94/1.16 [s_0](X) = X + 1/2 0.94/1.16 [big_0] = 0 0.94/1.16 [inf_1](X) = 2.X + 2 0.94/1.16 [S_0](X) = 1/2.X + 1/2 0.94/1.16 0.94/1.16 Problem 1.1: 0.94/1.16 0.94/1.16 SCC Processor: 0.94/1.16 -> Pairs: 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 ->Strongly Connected Components: 0.94/1.16 ->->Cycle: 0.94/1.16 ->->-> Pairs: 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 ->->-> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 ->->-> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 0.94/1.16 Problem 1.1: 0.94/1.16 0.94/1.16 Reduction Pairs Processor: 0.94/1.16 -> Pairs: 0.94/1.16 S_0(inf_1(x)) -> x 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 -> Usable rules: 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 ->Interpretation type: 0.94/1.16 Linear 0.94/1.16 ->Coefficients: 0.94/1.16 All rationals 0.94/1.16 ->Dimension: 0.94/1.16 1 0.94/1.16 ->Bound: 0.94/1.16 2 0.94/1.16 ->Interpretation: 0.94/1.16 0.94/1.16 [cons_0](X1,X2) = X1 + 1/2.X2 + 1/2 0.94/1.16 [cons_1](X1,X2) = 1/2.X2 0.94/1.16 [s_0](X) = X 0.94/1.16 [big_0] = 0 0.94/1.16 [inf_1](X) = 2.X + 2 0.94/1.16 [S_0](X) = X 0.94/1.16 0.94/1.16 Problem 1.1: 0.94/1.16 0.94/1.16 Basic Processor: 0.94/1.16 -> Pairs: 0.94/1.16 Empty 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 cons_0(x,inf_1(s_0(x4))) -> x4 0.94/1.16 cons_0(x4,inf_1(s_0(x))) -> x4 0.94/1.16 s_0(x) -> S_0(x) 0.94/1.16 -> Result: 0.94/1.16 Set P is empty 0.94/1.16 0.94/1.16 The problem is finite. 0.94/1.16 0.94/1.16 Problem 1.2: 0.94/1.16 0.94/1.16 Reduction Pairs Processor: 0.94/1.16 -> Pairs: 0.94/1.16 *TOP*_0(inf_1(x)) -> *TOP*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 Empty 0.94/1.16 -> Usable rules: 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 ->Interpretation type: 0.94/1.16 Linear 0.94/1.16 ->Coefficients: 0.94/1.16 Natural Numbers 0.94/1.16 ->Dimension: 0.94/1.16 1 0.94/1.16 ->Bound: 0.94/1.16 2 0.94/1.16 ->Interpretation: 0.94/1.16 0.94/1.16 [cons_0](X1,X2) = 0 0.94/1.16 [cons_1](X1,X2) = 2.X2 0.94/1.16 [s_0](X) = 1 0.94/1.16 [big_0] = 0 0.94/1.16 [inf_1](X) = 2 0.94/1.16 [*TOP*_0](X) = 2.X 0.94/1.16 0.94/1.16 Problem 1.2: 0.94/1.16 0.94/1.16 Basic Processor: 0.94/1.16 -> Pairs: 0.94/1.16 Empty 0.94/1.16 -> Rules: 0.94/1.16 *top*_0(inf_1(x)) -> *top*_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_0(inf_1(x),x0) -> cons_0(cons_0(x,inf_1(s_0(x))),x0) 0.94/1.16 cons_0(x0,inf_1(x)) -> cons_1(x0,cons_0(x,inf_1(s_0(x)))) 0.94/1.16 cons_1(x,cons_0(y,z)) -> big_0 0.94/1.16 cons_1(x,cons_1(y,z)) -> big_0 0.94/1.16 s_0(inf_1(x)) -> s_0(cons_0(x,inf_1(s_0(x)))) 0.94/1.16 -> Unhiding rules: 0.94/1.16 Empty 0.94/1.16 -> Result: 0.94/1.16 Set P is empty 0.94/1.16 0.94/1.16 The problem is finite. 0.94/1.16 EOF